Probably save a few bucks by dropping the CPU cooler and going with the stock heatsink. You're not overclocking so it's fine. If your mom doesn't care about how the case looks, you can probably get a cheaper case. Again, you don't have high end parts so heat won't really be an issue.

If you go with an RX 460 for the GPU, it would also shave off more money, but I have no idea how well that GPU performs or if it's enough for Dolphin at 1080p.

But in any case, the CPU you listed will run Dolphin's JIT extremely well for most games in Dolphin.